Question

4. In the adjoining figure, PT is a tangent to the circle with centre C. Given CP = 20 cm and PT = 16 cm, find the radius of the circle. P​

Answer 1

12cm

Given :

• PT(a tangent) = 16cm
• CP( distance from the centre to the point p ) = 20cm

To find :

• Radius of the circle = CT

Solution :

We know that, a tangent forms an angle measuring 90° right where it touches the circle,

Therefore,

Using Pythagoras theorem,

• Base = √[(hypotenuse)²-(perpendicular)²]
• CT = √[(20cm)²-(16cm)²]
• CT = √(400cm²-256cm²)
• CT = √(144cm²)
• CT = 12cm

Therefore,the measure of the radius of the mentioned circle would be equal to 12cm.

Answer 2

Radius = 12 cm

Explanation:

Note:

In geometry, a tangent is a line that touches a circle at exactly one point. The point of contact is called the point of tangency. The tangent line is perpendicular to the radius drawn to the point of tangency.

For the Question:

In the given figure, CP is the radius of the circle.

Given:

• CP = 20 cm
• PT = 16 cm.

To find:

• Radius of the circle.

Solution:

Since PT is a tangent to the circle, CP is perpendicular to PT.

Therefore, in triangle PCT is right angled triangle.

In right angled triangle PCT

• Hypotenuse = PC = 20 cm
• Base = PT = 16 cm
• Perpendicular = TC = radius = ?

Now,

We can use Pythagoras theorem,

`\sf Hypotenuse^2 = base^2 + Perpendicular^2`

`\sf CP^2 = PT^2 + PC^2`

`\sf 20^2 = 16^2 + PC^2`

`\sf PC^2 = 20^2 - 16^2`

`\sf PC^2 = 640 - 256`

`\sf PC^2 = 144`

`\sf PC =√(144)`

`\sf PC = 12 cm`

Therefore, the radius of the circle is 12 cm.